Name: Chapter 6: Systems of Linear Equations and Inequalities

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Lesson 6-1: Graphing Systems of Equations Date:

Example 1: Use the graph to determine whether each system is consistent or inconsistent and if it is

independent or dependent.

a. 𝑦 = −𝑥 − 1 and 𝑦 = 𝑥 + 1

b. 𝑦 = −𝑥 − 1 and 𝑦 = −𝑥 + 2

c. 𝑦 = −𝑥 − 1 and 3𝑥 + 3𝑦 = −3

Example 2: Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

A. 𝑦 = 2𝑥 + 3 and 8𝑥 − 4𝑦 = −12

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Name: Chapter 6: Systems of Linear Equations and Inequalities

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Example 2: Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

B. 𝑥 − 𝑦 = 2 and 3𝑦 + 2𝑥 = 9

Example 3: Natalie rode 20 miles last week and plans to ride 35 miles per week. Dan rode 50 miles last week and plans to ride 25 miles per week. Predict the week in which Natalie and Dan will have ridden the same number of miles.

Step 1: Write an equation for the number of miles Natalie rides her bike.

Step 2: Write an equation for the number of miles Dan rides his bike.

Step 3: Graph both equations.

Step 4: Estimate the point at which the graphs intersect.

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Name: Chapter 6: Systems of Linear Equations and Inequalities

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Lesson 6-2: Substitution Date:

Example 1: Use substitution to solve the system of equations.

𝑥 − 2𝑦 = −3

3𝑥 + 5𝑦 = 24

Example 2: Solve the system of equations twice using the substitution method.

Name: Chapter 6: Systems of Linear Equations and Inequalities

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Example 3: Use substitution to solve the system of equations.

2𝑥 + 2𝑦 = 8

𝑥 + 𝑦 = −2

Example 4: A nature center charges $35.25 for a yearly membership and $6.25 for a single admission. Last week it sold a combined total of 50 yearly memberships and single admissions for $660.50. How many memberships and how many single admissions were sold?

Name: Chapter 6: Systems of Linear Equations and Inequalities

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Lesson 6-3: Elimination Using Addition and Subtraction Date:

Example 1: Use elimination to solve the system of equations.

−3𝑥 + 4𝑦 = 12

3𝑥 − 6𝑦 = 18

Example 2: Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

Name: Chapter 6: Systems of Linear Equations and Inequalities

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Example 3: Use elimination to solve the system of equations.

4𝑥 + 2𝑦 = 28

4𝑥 − 3𝑦 = 18

Example 4: A hardware store earned $956.50 from renting ladders and power tools last week. The store charged 36 days for ladders and 85 days for power tools. This week the store charged 36 days for ladders, 70 days for power tools, and earned $829. How much does the store charge per day for ladders and for power tools?

Name: Chapter 6: Systems of Linear Equations and Inequalities

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Lesson 6-4: Elimination Using Multiplication Date:

Example 1: Use elimination to solve the system of equations.

2𝑥 + 𝑦 = 23

3𝑥 + 2𝑦 = 37

Example 2: Use elimination to solve the system of equations.

4𝑥 + 3𝑦 = 8

3𝑥 − 5𝑦 = −23

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Example 3: A fishing boat travels 10 miles downstream in 30 minutes. The return trip takes the boat 40 minutes. Find the rate in miles per hour of the boat in still water.

Let 𝑏 =

Let 𝑐 =

𝑟 𝑡 𝑑 𝑑 = 𝑟𝑡

Down-stream

Return

Name: Chapter 6: Systems of Linear Equations and Inequalities

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Lesson 6-5: Applying Systems of Linear Equations Date:

Example 1: Determine the best method to solve the system of equations. Then solve the system.

A. 2𝑥 + 3𝑦 = 23

4𝑥 + 2𝑦 = 34

B. At the school pool party, Mr. Lewis bought 1 adult ticket and 2 child tickets for $10. Mrs. Vroom bought 2 adult tickets and 3 child tickets for $17. Determine the best method to solve the system of equations. Then solve the system.

Name: Chapter 6: Systems of Linear Equations and Inequalities

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Example2:

A. Ace Car Rental rents a car for $45 and $0.25 per mile. Star Car Rental rents a car for $35 and $0.30 per mile. How many miles would a driver need to drive before the cost of renting a car at Ace Car Rental and renting a car at Star Car Rental were the same?

B. The cost to rent a video game from Action Video is $2 plus $0.50 per day. The cost to rent a video game at TeeVee Rentals is $1 plus $0.75 per day. After how many days will the cost of renting a video game at Action Video be the same as the cost of renting a video game at TeeVee Rentals?

Name: Chapter 6: Systems of Linear Equations and Inequalities

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Lesson 6-6: Systems of Inequalities Date:

Example 1: Solve the system of inequalities by graphing.

A. 𝑦 < 2𝑥 + 2

𝑦 ≥ −𝑥 − 3

B. 2𝑥 + 𝑦 ≥ 4

𝑥 + 2𝑦 > −4

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Example 2: Solve the system of inequalities by graphing.

𝑦 ≥ −3𝑥 + 1

𝑦 ≤ −3𝑥 + 2

Example 3:

A. SERVICE A college service organization requires that its members maintain at least a 3.0 grade point average, and volunteer at least 10 hours a week. Define the variables and write a system of inequalities to represent this situation. Then graph the system.

B. Name one possible solution.

C. Is (3.5, 8) a solution?

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